Exact spectrum of the spin-s Heisenberg chain with generic non-diagonal boundaries

Based on the inhomogeneous T − Q relation constructed via the off-diagonal Bethe Ansatz, the Bethetype eigenstates of the XXZ spin-1 2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T − Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations.

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“…The relation was then confirmed by the SoV method[41] for the XXZ case and its generalization to higher spin case was given in[40,42].…”

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confidence: 92%

Bethe states of the XXZ spin-12chain with arbitrary boundary fields

et al. 2015

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“…With the help of proposed inhomogeneous T − Q relations, the exact solutions of some typical models with off-diagonal boundary reflections are obtained [18]. Furthermore, in order to solve the models with high ranks [19][20][21][22][23][24][25], the nested ODBA is proposed and the exact solutions of models associated with A n [26,27], A…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the $C_n$ quantum spin chain

Li,

Xue,

Sun

et al. 2020

Preprint

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We study the exact solutions of quantum integrable model associated with the C n Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the C 3 as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processes. Based on the resulted operator product identities among fused transfer matrices and some necessary additional constraints such as asymptotic behaviors and relations at some special points, we obtain the eigenvalues of transfer matrices and parameterize them as homogeneous T − Q relations in the periodic case or inhomogeneous ones in the open case. We also give the exact solutions of the C n model with an off-diagonal open boundary condition. The method and results in this paper can be generalized to other high rank integrable models associated with other Lie algebras.

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“…A remarkable one is the off-diagonal Bethe ansatz (ODBA) [16,17], which allow us to construct the exact spectrum systematically. The nested ODBA has also been developed to deal with the models with different Lie algebras such as A n [22,23], A…”

Section: Introductionmentioning

confidence: 99%

Graded Off-diagonal Bethe ansatz solution of the $SU(2|2)$ spin chain model with generic integrable boundaries

Xu,

Cao,

Qiao

et al. 2020

Preprint

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The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the SU (2|2) vertex model with both periodic and generic open boundary conditions are constructed. By generalizing the fusion techniques to the supersymmetric case, a closed set of operator product identities about the transfer matrices are derived, which allows us to give the eigenvalues in terms of homogeneous or inhomogeneous T − Q relations. The method and results provided in this paper can be generalized to other high rank supersymmetric quantum integrable models.

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Exact spectrum of the spin-s Heisenberg chain with generic non-diagonal boundaries

Cited by 18 publications

References 80 publications

Bethe states of the XXZ spin-12chain with arbitrary boundary fields

Bethe states of the XXZ spin-12chain with arbitrary boundary fields

Exact solutions of the $C_n$ quantum spin chain

Graded Off-diagonal Bethe ansatz solution of the $SU(2|2)$ spin chain model with generic integrable boundaries

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